Seminara za unitarne reprezentacije i automorfne forme

Jan Frahm, Aarhus University, Danska

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Analytic continuation of branching laws for unitary representations

 

Abstract: Branching problems ask for the behaviour of the restriction of
an irreducible representation of a group $G$ to a subgroup $H$. In the
context of smooth representations of real reductive groups, this
typically leads to the study of multiplicities with which an irreducible
representation of $H$ occurs as a quotient of an irreducible
representation of $G$. Here, both quantitative results such as
multiplicity-one theorems and qualitative results such as the
Gan-Gross-Prasad conjectures are of interest.
In the context of unitary representations of real reductive groups, one
can go a step further and explicitly decompose an irreducible
representation of $G$ into a direct integral of irreducible
representations of $H$. I will explain how branching laws for unitary
representations are related to those in the smooth category, and how one
can use an analytic continuation procedure along a principal series
parameter to obtain explicit branching laws from certain Plancherel
formulas for homogeneous spaces.

 

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Marcela Hanzer